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Approximate factor models with weaker loadings

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  • Bai, Jushan
  • Ng, Serena

Abstract

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where Λ0′Λ0/Nα is positive definite in the limit when α=1, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when α∈(0,1] albeit at slower rates and under additional assumptions on the sample size. The results hold whether α is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.

Suggested Citation

  • Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1893-1916
    DOI: 10.1016/j.jeconom.2023.01.027
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    Citations

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    Cited by:

    1. Matteo Barigozzi & Marc Hallin, 2024. "The Dynamic, the Static, and the Weak Factor Models and the Analysis of High-Dimensional Time Series," Working Papers ECARES 2024-14, ULB -- Universite Libre de Bruxelles.
    2. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org, revised Nov 2024.
    3. Luca Margaritella & Ovidijus Stauskas, 2024. "New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings," Papers 2409.20415, arXiv.org, revised Oct 2024.
    4. Jianqing Fan & Yuling Yan & Yuheng Zheng, 2024. "When can weak latent factors be statistically inferred?," Papers 2407.03616, arXiv.org, revised Sep 2024.
    5. Jungjun Choi & Ming Yuan, 2024. "High Dimensional Factor Analysis with Weak Factors," Papers 2402.05789, arXiv.org.
    6. Bin Peng & Liangjun Su & Yayi Yan, 2024. "A Robust Residual-Based Test for Structural Changes in Factor Models," Papers 2406.00941, arXiv.org.
    7. Jad Beyhum, 2024. "Counterfactuals in factor models," Papers 2401.03293, arXiv.org.
    8. Wanbo Lu & Guanglin Huang & Kris Boudt, 2024. "Estimation of Non-Gaussian Factors Using Higher-order Multi-cumulants in Weak Factor Models," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 24/1085, Ghent University, Faculty of Economics and Business Administration.
    9. Lihua Lei & Brad Ross, 2023. "Estimating Counterfactual Matrix Means with Short Panel Data," Papers 2312.07520, arXiv.org, revised May 2024.
    10. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson & Yaping Wang, 2024. "Performance of Empirical Risk Minimization For Principal Component Regression," Papers 2409.03606, arXiv.org, revised Sep 2024.
    11. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Models without Estimating the Rank," Papers 2311.16440, arXiv.org, revised Oct 2024.
    12. De Vos, Ignace & Stauskas, Ovidijus, 2024. "Cross-section bootstrap for CCE regressions," Journal of Econometrics, Elsevier, vol. 240(1).
    13. Diego Fresoli & Pilar Poncela & Esther Ruiz, 2024. "Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors," Papers 2407.06883, arXiv.org.

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    More about this item

    Keywords

    Principal components; Low rank decomposition; Weak factors; Factor augmented regressions;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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